Physics · Ch 6 — Work, Energy and Power

Summary

Work is done when a force causes displacement: $W = \vec{F} \cdot \vec{s} = F s \cos\theta$ . Work is a scalar; it is positive if $\theta < 90^\circ$ , zero if $\theta = 90^\circ$ , and negative if $\theta > 90^\circ$ .
Kinetic energy of a body of mass $m$ moving with speed $v$ is $K = \frac{1}{2} m v^2$ . The work-energy theorem states that the net work done on a body equals its change in kinetic energy: $W_{\text{net}} = \Delta K$ .
Potential energy is stored energy due to configuration. For gravity near Earth's surface: $U_g = mgh$ (taking $U=0$ at $h=0$ ). For a spring obeying Hooke's law: $U_s = \frac{1}{2} k x^2$ , where $x$ is the displacement from natural length.
Conservative forces (e.g., gravity, spring force) have work independent of path; the work done around a closed loop is zero. For a conservative force, $W_c = -\Delta U$ . Non-conservative forces (e.g., friction) dissipate energy as heat; their work depends on path.
Mechanical energy $E = K + U$ is conserved if only conservative forces act: $K_i + U_i = K_f + U_f$ . If non-conservative forces do work, $W_{nc} = \Delta E$ .
Power is the rate of doing work: $P = \frac{dW}{dt}$ . For a constant force and velocity, $P = \vec{F} \cdot \vec{v}$ . The SI unit is the watt (W); 1 W = 1 J/s. …